Question

Assume that today you deposit Rs. 6,000 in a savings account that pays 8.5%.

a. If the bank compounds interest annually, how much will you have in the savings account after 5 years?
b. What will be the balance in the savings account after 5 years if the bank used quarterly compounding rather than annual compounding?
c. What will be the balance in the savings account after 5 years if the bank used monthly compounding rather than annual compounding?
d. Suppose you deposited the Rs. 6,000 in six payments of Rs. 1000 each in years 1 to 6. How much would you have in your account at the end of year 5, if the annual interest rate is 8.5%?

Answer 1

a. With annual compounding, the balance after 5 years will be Rs. 8,464.47. b. With quarterly compounding, the balance after 5 years will be Rs. 8,529.50. c. With monthly compounding, the balance after 5 years will be Rs. 8,570.84. d. If you deposit Rs. 1,000 each year for 6 years, the balance at the end of year 5 will be Rs. 6,684.88.

Step-by-step explanation:

a. To calculate the balance after 5 years with annual compounding, we use the formula:

Balance = Principal * (1 + interest rate)^n

where Principal = Rs. 6,000, interest rate = 8.5% = 0.085, and n = 5 (years). Plugging these values into the formula, we get:

Balance = 6,000 * (1 + 0.085)^5 = Rs. 8,464.47

b. For quarterly compounding, we need to divide the interest rate by 4 and multiply the number of years by 4. So, the formula becomes:

Balance = 6,000 * (1 + 0.085/4)^(5*4) = Rs. 8,529.50

c. For monthly compounding, we need to divide the interest rate by 12 and multiply the number of years by 12. So, the formula becomes:

Balance = 6,000 * (1 + 0.085/12)^(5*12) = Rs. 8,570.84

d. If you deposit Rs. 1,000 each year for 6 years, the formula becomes:

Balance = (1,000 * (1 + 0.085))^5 + (1,000 * (1 + 0.085))^4 + ... + (1,000 * (1 + 0.085)) = Rs. 6,684.88